Unfortunately, it seems that FD have indeed mixed up ther terminology and used "magma" instead of "lava". "Magma" appears on planets with "major volcanism" (which I believe is the journal teminology for it), but for "minor volcanism", we have the word "geysers" instead of "magma". And "geysers" are definitely surface features.
No, lava is magma ones it's expelled to the surface, magma is subsurface vulcanism. Vulcanism often occurs on planets without a molton core and is usually caused by gravitational stress or heating by a stellar source and will usually be restricted to certain areas for instance where the fractures provide a path to the surface. So water geysers will appear on a cold world without a molton core in areas where gravitational stress fractures are grinding together and heating the ice to the boiling point, but these worlds by definition don't have magma, so because they don't have molten magma zone below the surface so they don't have a defined magma type, just a vulcanism type.
Major vulcanism may sometimes be associated with a magma subsurface zone but I have always associated it with the number of features since I first started exploring volcanic sites when they were brought out as a feature by FDEV. For instance cold bodies in close orbit around a gas giant will often have major vulcanism where identical bodies further out that aren't under as much stress will have fewer surface features and be described as having minor vulcanism, but the vulcanism type should never be descriped as magma. The terms major and minor vulcanism labels, and the unstated ones out there aren't associated with magma but with the number of surface features, that's been clear from early exploration of vulcanism. Bodies with a few sites will be minor, bodies with an intermediate number will be unspecified and bodies with a lot will be major.
At lease that's the way it has been up until the release of the FSS and the codex. I haven't looked into it since then but I have assumed it has not changed. I will check out my next few systems with vulcanism to see if it is still the same.
Of course most large bodies, up around the 6,000+klm radius, if they have vulcanism, should be almost always be defined by a magma type because like the earth they should still have a molten core, I will have to check that out as well. It may be that they have changed their descriptions since the release of the FSS and codex, but I see no reason why.
